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PreprintCC BY-NC-ND 4.0HAL

On the doubling of variables technique in first order Hamilton-Jacobi equations

  • Charles Bertucci
  • Giacomo Ceccherini Silberstein
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Abstract

In this paper, we revisit the technique of doubling variables in first order Hamilton-Jacobi equations, especially when the equations arise in optimal control. We show that by tuning the penalization between the two points, we can change drastically the proof, somehow shifting the regularity hypotheses into geometrical properties of the penalization. We present this idea in a finite dimensional setting and then exploit it on equations posed on Wasserstein spaces.

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Cite

BibTeXRIS
BibTeX
@misc{bertucci2026doubling,
  title = {{On the doubling of variables technique in first order Hamilton-Jacobi equations}},
  author = {Charles Bertucci and Giacomo Ceccherini Silberstein},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  eprint = {2512.03652},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05394167v2},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - On the doubling of variables technique in first order Hamilton-Jacobi equations
AU  - Charles Bertucci
AU  - Giacomo Ceccherini Silberstein
PY  - 2026
DA  - 2026/09/03
PB  - HAL
UR  - https://hal.science/hal-05394167v2
AB  - In this paper, we revisit the technique of doubling variables in first order Hamilton-Jacobi equations, especially when the equations arise in optimal control. We show that by tuning the penalization between the two points, we can change drastically the proof, somehow shifting the regularity hypotheses into geometrical properties of the penalization. We present this idea in a finite dimensional setting and then exploit it on equations posed on Wasserstein spaces.
ER  -